Streater, R. F. Statistical dynamics with thermal noise. (English) Zbl 0822.60093 Etheridge, Alison (ed.), Stochastic partial differential equations. Proceedings of an ICMS workshop held in Edinburgh, UK in March 1994. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 216, 262-286 (1995). Summary: We consider how to add noise to a nonlinear system in a way that obeys the laws of thermodynamics. We treat a class of dynamical systems which can be expressed as a (possibly nonlinear) motion through the set of probability measures on a sample space. Thermal noise is added by coupling this random system to a heat-particle distributed according to a Gibbs state. The theory is illustrated by the Brussellator, where it is shown that the noise converts a limit cycle into a global attractor. In the linear case it is shown that every Markov chain with transition matrix close to the identity is obtained by coupling to thermal noise with a bistochastic transition matrix.For the entire collection see [Zbl 0817.00017]. Cited in 12 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B31 Stochastic methods applied to problems in equilibrium statistical mechanics Keywords:thermodynamics; coupling; Gibbs state; Brussellator; bistochastic transition matrix PDFBibTeX XMLCite \textit{R. F. Streater}, Lond. Math. Soc. Lect. Note Ser. 216, 262--286 (1995; Zbl 0822.60093)